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Solute transport parallel to an interface separating two different porous materials
Author(s) -
Van Duijn C. J.,
Zee S. E. A. T. M.
Publication year - 1986
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr022i013p01779
Subject(s) - dispersion (optics) , mechanics , flow (mathematics) , porous medium , boundary value problem , transversal (combinatorics) , zero (linguistics) , boundary (topology) , materials science , porosity , mathematics , thermodynamics , mathematical analysis , physics , optics , composite material , linguistics , philosophy
The transport of solute is studied for a flow domain consisting of two regions that are separated by a sharp interface parallel to the direction of water flow. The two regions have different flow velocities, linear adsorption coefficients, and porosities. An approximate analytical solution is given for the depletion of solute in the most permeable region caused by transfer of solute into the less permeable region. To take into account the boundary conditions at the interface, an approximate expression is derived for the concentration at the interface. In the derivations the longitudinal dispersion coefficient is assumed to be zero, and the transversal dispersion coefficient is taken finite. For comparison to numerical results, an expression for the concentration averaged over the height in the permeable region, at given distance and time, is presented. The agreement of numerically obtained breakthrough curves and interface concentrations with the analytical results is shown. Because of the zero longitudinal dispersion coefficient in the analytical approach, differences occur at initial breakthrough. Agreement between numerical and analytical results is good after initial breakthrough provided the assumption of two infinitely thick regions is valid. Lower bound constraints for the thickness of the two regions are given. The assumption made often of infinite transversal dispersion leads to significant differences compared to numerical results in the case of a large retardation factor R 2 in the region with the smallest transport velocity.